He has the smoothest, silkiest tone. He’s the Nat King Cole of sax tones.
ETA: Paintcharge - I think they dug the Echoman Delay, and got Bunny as a cool reggae name, so they were going to be Bunny and the Echomen, but some poster got printed wrong and the reversed name stuck. I just checked Wikipedia though and they just said it was one of a few silly names they came up with.
Freddie the Flute from H.R Puffinstuff.
B.B. King’s Lucille.
To the best of my recollection, that was a guitar.
And in any case, it wasn’t a single instrument. That was the name BB gave to all his guitars.
I was going to say what drum machine, but looking on Wikipedia, it looks like the early incarnation of the band did, indeed have a drum machine. It also says that it is widely assumed to be the “Echo” of “Echo and the Bunnymen,” but the band denies it.
Ronald Mael of Sparks has always rearranged the letters of the brand name on the back of his keyboard from “Roland” to “Ronald”, but I’m not sure that’s what he’s calling the keyboard. 
I was sure I saw a documentary on Stringbean somewhere that mentioned his banjo having a name, but I can’t find any references to it anywhere, so I must be mis-remembering that alternative fact.
Grandmaster Flash calls his two turntables The Wheels of Steel: The Adventures Of Grandmaster Flash On The Wheels Of Steel - YouTube
Yes he named all his guitars Lucille. The original one was a cheap Gibson that I believe is lost to history. Through most of his later career he played Gibson ES-355s until Gibson started to make a special Lucille model which was basically a solid body ES-355. King used to stuff tags in the f-holes of the 355 to reduce feedback.
Eric Clapton had Blackie, a guitar he cobbled together from three vintage Fender Stratocasters. In 2004, she fetched almost a million dollars in a charity auction for Clapton’s rehab center.
Loach - Not solid body. Still semi-hollow, but no F-Holes.
Again, named guitars are all over the place and excluded by the OP.
…and, of course, I didn’t read the OP very well. Oy, gevalt.
**Shakester **took my first idea with Doktor Avalanche, so there goes my first crack at redemption.
Francis Vaughn, I had the same idea you had with organs. The Curtis Organ at the University of Pennsylvania comes to mind. The Wanamaker Organ in Philadelphia might qualify, too. It was named for its location in Wanamaker’s Department Store. The store is now a Macy’s, but the organ retains its maiden name.
Oleg Bernov of the Red Elvises once told me the name of his goofy bass.(which produces really good sound)
IIRC, the name was in Russian. Anyway, I do not remember what he told me.
Does the instrument of Futureman (from Bela Fleck and the Flecktones) count? He played something called a drumitar.
As far as I know, there is (or was) only one of them, so really, it’s the drumitar. Which is almost giving it a name.
Keyboard magazine christened Keith Emerson’s modular Moog “The World’s Most Dangerous Synth”. Not really a name, but pretty much anyone in the prog or synth world would immediately know what you are talking about if you use that term.
Drumitar is a general name for the class of instruments, I guess, as there are other similar instruments out there in the world. His is the Synthaxe, if you want to give it a singular name.
Similarly, Junior Brown has his Guit-Steel, but now they are selling versions of it so his instrument can’t really be considered a named instrument anymore.
It’s hard to distinguish between the band and the instrument, but Matt Lorenz of The Suitcase Junket plays the oddball collection of one man band instruments that might as well be called a single instrument. It’s a combination of the guitar and the various percussion objects he plays with his feet, amplifiers, and Tuvan throat singing. So, the Suitcase Junket is a singular, named instrument.
I knew of a band (The Shoppe) that called their drum machine “Chip.”
TONTO, the custom-built synthesizer of Tonto’s Expanding Head Band.
The band/duo wasn’t very famous for their own output, but worked with Stevie Wonder on some his most famous and best seventies albums.
A few that come to mind in the world of bluegrass, Sam Bush’s 1937 Gibson F-5 mandolin is known as “Hoss,” and David Grisman’s 1922 Gibson Loar F-5 mandolin is named “Crusher.” And while it’s a serial number and not strictly a mandolin’s name, “73987” has particular resonance in the bluegrass world. (Same with “58957,” though that’s a guitar…)
